The transformer

1. Overview

A transformer is an electrical device used to change the voltage of an alternating current (AC). By increasing or decreasing voltages, transformers allow electricity to be transmitted efficiently over long distances, minimizing energy loss in the form of heat.

Key Definitions

• Primary Coil: The input coil of a transformer, connected to the AC power supply.
• Secondary Coil: The output coil of a transformer, where the transformed voltage is delivered to the load.
• Soft-Iron Core: A ferromagnetic core that links the magnetic field of the primary coil to the secondary coil.
• Step-up Transformer: A transformer that increases the voltage (has more turns on the secondary coil than the primary).
• Step-down Transformer: A transformer that decreases the voltage (has fewer turns on the secondary coil than the primary).

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Core Content

Construction of a Simple Transformer

A simple transformer consists of two coils of insulated wire (the primary and secondary) wound around a laminated soft-iron core.

• The coils are not electrically connected to each other.
• The soft-iron core is used because it is easily magnetized and demagnetized, which helps concentrate the magnetic field.

The Transformer Equation

The ratio of the voltages is equal to the ratio of the number of turns on the coils: $$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$

• Where $V$ is voltage and $N$ is the number of turns.
• Step-up: $N_s > N_p$, therefore $V_s > V_p$.
• Step-down: $N_s < N_p$, therefore $V_s < V_p$.

Worked Example: A transformer has 200 turns on the primary coil and 4000 turns on the secondary coil. If the input voltage is 12V, calculate the output voltage.

1. Identify: $V_p = 12$, $N_p = 200$, $N_s = 4000$.
2. Rearrange: $V_s = V_p \times (\frac{N_s}{N_p})$
3. Calculate: $V_s = 12 \times (\frac{4000}{200}) = 12 \times 20 = 240\text{V}$.

High-Voltage Transmission

Electricity is transported from power stations to homes via the National Grid.

1. Step-up transformers increase the voltage to very high levels (e.g., 400,000V) for long-distance transmission.
2. Step-down transformers decrease the voltage to safe levels (e.g., 230V) for use in homes.

Advantages of High-Voltage Transmission:

• By increasing the voltage, the current in the cables is reduced.
• Lower current results in significantly less energy being lost as heat in the transmission wires.
• This makes the process more efficient and cheaper.

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Extended Content (Extended Only)

Principle of Operation

1. An alternating current (AC) flows through the primary coil.
2. This creates a constantly changing magnetic field within the primary coil.
3. The soft-iron core directs this changing magnetic field through the secondary coil.
4. The changing magnetic field cuts through the secondary coil, inducing an alternating e.m.f. (voltage) in it via electromagnetic induction. Note: Transformers do NOT work with Direct Current (DC) because DC produces a steady magnetic field that does not induce a voltage.

100% Efficiency Equation

For an ideal transformer (100% efficient), the power input equals the power output: $$I_p V_p = I_s V_s$$ This means that if voltage is "stepped up," the current must be "stepped down" to conserve energy.

Worked Example: A transformer steps down 240V to 12V. If the output current is 2A, calculate the input current.

1. Identify: $V_p = 240$, $V_s = 12$, $I_s = 2$.
2. Equation: $I_p \times 240 = 2 \times 12$
3. Calculate: $I_p = \frac{24}{240} = 0.1\text{A}$.

Power Loss in Cables

The power lost as heat in a wire is given by: $$P = I^2 R$$

• Because the power loss is proportional to the square of the current, even a small reduction in current leads to a massive reduction in power loss.
• By using a transformer to increase voltage, the current $I$ decreases, which minimizes the $I^2 R$ "heating loss" in long-distance cables.

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Key Equations

Equation	Symbols	Units
$\frac{V_p}{V_s} = \frac{N_p}{N_s}$	$V$=Voltage, $N$=Number of turns	V (Volts), No units for $N$
$I_p V_p = I_s V_s$	$I$=Current, $V$=Voltage	A (Amps), V (Volts)
$P = I^2 R$	$P$=Power loss, $I$=Current, $R$=Resistance	W (Watts), A (Amps), $\Omega$ (Ohms)

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Common Mistakes to Avoid

• ❌ Wrong: Inverting the voltage ratio (e.g., calculating $12 \times \frac{200}{4000}$ when you meant to step-up).
  • ✅ Right: Always check if your answer makes sense—if it's a step-up transformer, your output voltage must be higher than the input.
• ❌ Wrong: Assuming current remains the same in both coils.
  • ✅ Right: If voltage increases, current must decrease ($I_p V_p = I_s V_s$).
• ❌ Wrong: Using the power equation $P=VI$ to calculate power loss in cables without considering resistance.
  • ✅ Right: Use $P = I^2 R$ specifically when explaining why high voltage (low current) reduces energy loss.
• ❌ Wrong: Forgetting that transformers only work with alternating current (AC).
  • ✅ Right: State clearly that a changing magnetic field is required for induction.

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Exam Tips

1. Check the turns: If $N_s > N_p$, it is a step-up transformer. If $N_p > N_s$, it is a step-down transformer. Always state which one it is if asked.
2. Show your steps: In the Extended paper, you often need to calculate current after finding the voltage. Show the $V_p/V_s$ step first, then the $IV$ step.
3. The "Why" of High Voltage: If asked why we use high voltage for transmission, use the phrase: "Low current results in less energy lost as heat due to the resistance of the cables ($P=I^2R$)."